The values of t and s that satisfy the equality are t = sqrt(3 * 74.67 / 49) and s = sqrt(3 * 74.67 / 49).
The equality ⟨−(7t^2), 3s-2t⟩ = ⟨3s-t,24t⟩ means that the two vectors are equal, so the components must be equal:
-7t^2 = 3s-t
3s-2t = 24t
Solving for t, we can subtract 24t from both sides:
3s-26t = 0
Dividing both sides by 3, we get:
s - 8.67t = 0
So, t = s / 8.67.
Substituting t = s / 8.67 back into the first equation, we get:
-7(s / 8.67)^2 = 3s - s / 8.67
Expanding and simplifying, we get:
-49s^2 / 74.67 + 3s = s^2 / 74.67
Dividing both sides by s^2 / 74.67, we get:
-49 + 3 * 74.67 / s = 1
Multiplying both sides by s^2 / 74.67, we get:
-49s^2 + 3 * 74.67 = s^2
Expanding and rearranging, we get:
s^2 - 49s^2 + 3 * 74.67 = 0
Combining like terms, we get: -49s^2 + 3 * 74.67 = 0
Dividing both sides by -49, we get: s^2 = 3 * 74.67 / 49
Taking the square root of both sides, we get: s = sqrt(3 * 74.67 / 49)
Thus, the values of t and s that satisfy the equality are t = sqrt(3 * 74.67 / 49) and s = sqrt(3 * 74.67 / 49).
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foall the sides of a square is changing at the rate of negative 3 per second. when the side is 10. determine the rate of change of the area.
The rate of change of the area of square with side 10 and rate of change of side is -3 per second is -60.
We have, For all sides of a square is
Rate of changing per second = - 3
Let "x" be side of square. So, x = 10. We have to determine the rate of change of the area. So, Rate of change in side ,x per unit time = dx/dt = -3 . As we know, the area of a polygon is equals to total space occupied by shape or polygon.
So, Area of square, A = side × side . In this case, Area of square , A = x² --(1)
Differentiating equation (1) with respect to time "t",
=> dA/dt = d/dt ( x²)
=> dA/dt = 2x dx/dt ( using derivative formula )
here,dx/dt --> rate of changing of side of square
Substitute the value of dx/dt = -3 in above derivative, dA/dt = 2x dx/dt
=> dA/dt = 2x (-3)
=> dA/dt = 2×(10)(-3) ( since side, x = 10)
=> dA/dt = -60
Hence, required rate of change of area is -60.
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Under the right growing conditions, a particular
species of plant has a doubling time of 12 days. Suppose a
pasture contains 46 plants of this species. How many
plants will there be after 20, 65, and x days?
Based on the information, we can infer that after 20 days there will be 153 plants and after 65 days there will be 498 plants.
How to find the number of plants after 20 and 65 days?To find the number of plants that will be after 20 and 65 days we must take into account the number of initial plants and the number of days required for the plantation to double.
Every 12 days it doubles.Initial amount 46 plants.According to the above, we must make a rule of 3 as shown below:
12 - 92
20 -
= 20 * 92 / 12 = 153
12 - 92
65
= 65 * 92 / 12 = 498
According to the above, after 20 days there will be 153 plants and after 65 days there will be 498 plants.
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In circle J with the measure of minor arc HK= 58°, find m/HLK.
Answer: m/HLK = ??
Answer:
∠ HLK = 29°
Step-by-step explanation:
the measure of the inscribed angle HLK is half the measure of its intercepted arc, that is
∠ HLK = [tex]\frac{1}{2}[/tex] × HB = [tex]\frac{1}{2}[/tex] × 58°= 29°
Puzzle #4
Can you find the measure of the indicated angle and type the correct code? Please remember to type in ALL caps with no spaces. (it isn’t CBCA)
The solution of all the measures of the angles are,
1) m ∠A = 63°
2) m ∠B = 138°
3) m ∠C = 117°
4) m ∠D = 137.22°
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
In figure 1;
Measure of angle A and angle B are vertically opposite angle and hence both are equal to each other.
⇒ ∠A = ∠B
⇒ 2x + 35 = 8x - 49
⇒ 35 + 49 = 8x - 2x
⇒ 84 = 6x
⇒ x = 14
Thus, The value of m ∠A = 2x + 35
= 2×14 + 35
= 28 + 35
= 63°
2) By the figure, the sum of both indicated angle is 180°.
Hence, We get;
⇒ 10x - 18 + 15x + 48 = 180
⇒ 25x + 30 = 180
⇒ 25x = 180 - 30
⇒ 25x = 150
⇒ x = 6
Thus, The value of m ∠B = 15x + 48
= 15×6 + 48
= 90 + 48
= 138°
3) By the figure, Both angles are alternate angle of parallel lines and hence both are equal.
So, We get;
⇒ 7x + 5= 12x - 75
⇒ 5 + 75 = 12x - 7x
⇒ 80 = 5x
⇒ x = 16
Thus, The value of m ∠C = 7x + 5
= 7×16 + 5
= 112 + 5
= 117°
4) By the figure, the sum of both indicated angle is 180°.
Hence, We get;
⇒ 27x - 21 + 10x - 16 = 180
⇒ 37x - 37 = 180
⇒ 37x = 180 + 37
⇒ 37x = 217
⇒ x = 217/37
⇒ x = 5.86
Thus, The value of m ∠D = 27x - 21
= 27×5.86 - 21
= 158.22 - 21
= 137.22°
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Rocko paid 12.50 for 25 game tickets. Louisa paid 17.50 for 36 game tickets. What is the constant of proportionality
Answer:
To find the constant of proportionality between the cost of the game tickets and the number of tickets purchased, we can write an equation that represents the relationship between the two values. Let's call the constant of proportionality "k".
Step 1: Write an equation for Rocko's purchase:
12.50 = k * 25
Step 2: Solve for k:
k = 12.50 / 25 = 0.50
Step 3: Write an equation for Louisa's purchase:
17.50 = k * 36
Step 4: Substitute the value of k from step 2 into the equation:
17.50 = 0.50 * 36
Step 5: Check if the value of k is the same for both equations:
17.50 / 36 = 0.50
The constant of proportionality is 0.50, which means that for each additional game ticket purchased, the cost increases by $0.50.
plsss helppp meee anyonee plsss
Answer:
1) 111, 112
2) 12, 9
3) -12
4) 31, 32, 33
Step-by-step explanation:
1) n + (n+1) = 223
2n + 1 = 223
2n=222
n = 111 numbers: 111, 112
2) n + (n-3) = 21
2n - 3 = 21
2n=24
n=12 numbers: 12, 9
3) 2*(n+5) = n-2
2n + 10 = n - 2
n = -12 number: -12
4) n + (n+1) + (n+2) = 96
3n + 3 = 96
3n = 93
n=31 numbers: 31, 32, 33
Simplify the following algebraic expression:-
[tex]\mathrm {\cfrac{2}{3}\:y -2(\cfrac{4}{3}\:y+z)}[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{ORIGINAL equation:}[/tex]
[tex]\mathsf{\dfrac{2}{3}y - 2(\dfrac{4}{3}y + z)}[/tex]
[tex]\huge\textbf{DISTRIBUTE \boxed{\rm{\bf -2}} within the}\\\\\huge\textbf{parentheses:}[/tex]
[tex]\mathsf{\dfrac{2}{3}y - 2(\dfrac{4}{3}y + z)}[/tex]
[tex]\mathsf{= \dfrac{2}{3}y - 2(\dfrac{4}{3}y) - 2(z)}[/tex]
[tex]\mathsf{= \dfrac{2}{3}y - \dfrac{8}{3}y - 2z}[/tex]
[tex]\huge\textbf{COMBINE the like terms:}[/tex]
[tex]\mathsf{= (\dfrac{2}{3}y - \dfrac{8}{3}y) - (2z)}[/tex]
[tex]\mathsf{= \dfrac{2}{3}y - \dfrac{8}{3}y - 2z}[/tex]
[tex]\mathsf{-2y - 2z}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{-2y - 2z}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
What method proves this two triangles congruent?
On solving the provided question we can say that so by SAS triangles are congruent
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
here,
BC = HI
AB = HG
angle ABC = IHG
so by SAS triangles are congruent
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let f(x) be a polynomial function such that f(3)=−2,f′(3)=0 and f′′(3)=−2. classify the point (3,−2).
The point (3, -2) can be classified as a local maximum of the polynomial function f(x).
What is polynomial ?
A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
In this case, the values f(3) = -2, f'(3) = 0, and f''(3) = -2 give us information about the graph of the polynomial function f(x) at the point x = 3.
First, f(3) = -2 means that the y-coordinate of the point (3, -2) is -2, so the point (3, -2) is on the graph of f(x).
Second, f'(3) = 0 means that the slope of the tangent line to the graph of f(x) at the point x = 3 is 0. This means that at x = 3, the graph of f(x) has a horizontal tangent line, which is a sign of a local maximum or minimum of the function.
Third, f''(3) = -2 means that the second derivative of f(x) at x = 3 is -2. This means that the graph of f(x) is concave down at x = 3. A concave down graph means that the function is decreasing at x = 3, so the point (3, -2) is a local maximum of the function.
Therefore, the point (3, -2) can be classified as a local maximum of the polynomial function f(x).
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What number is halfway between -38.7 and -38.71?
Answer: -38.705
Step-by-step explanation:
(-38.71) - (-38.7)
= -38.71 + 38.7
= -0.01
-0.01 ÷ 2 = -0.005
Then add it to -38.7:
= (-0.005) + (-38.7)
= -0.005 + 38.7
= -38.705
Amir puts £1390 into an bank account.
The account pays 2.25% compound interest each year.
Work out how much Amir will have in the account after 23 years.
Answer: look below love :))
Step-by-step explanation: To find out how much Amir will have in the account after 23 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A is the final amount
P is the initial principal (the amount Amir deposited)
r is the annual interest rate (2.25%)
n is the number of times the interest is compounded per year (let's assume it is compounded annually)
t is the number of years
So, we can plug in the given values:
A = 1390(1 + 0.0225)^(1*23)
A = 1390(1.0225)^(23)
A = 1390 * 2.6388955
A = 3655.922
So Amir will have £3655.922 in the account after 23 years with 2.25% compound interest.
HOW MANY 6- digit numbers are in the form 225A7B such that the number is divisible by 36? Please answer ASAP!!
There are three 6- digit numbers divisible by 36.
What is divisibility Rule?To decide if a fraction has to be decreased, dividesibility rules can be applied. The patterns that appear when we list the multiples of any number serve as the foundation for the rules.
Given:
We have 225A7B
Now, we will substitute A and B 0, 1 , 2.....9 to get the combination.
Also, A number is divisible by 36 if the number is divisible by 4 and 9.
So, take A=0 and B= 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
225070 is not divisible by 4 thus not divisible by 36.
and, 225071 is not divisible by 4 thus not divisible by 36.
and, 225072 is divisible by 4 and 9 thus divisible by 36.
and, 225073 is not divisible by 4 thus not divisible by 36.
and, 225074 is not divisible by 4 thus not divisible by 36.
and, 225075 is not divisible by 4 thus not divisible by 36.
and, 225076 is not divisible by 4 thus not divisible by 36.
and, 225077 is not divisible by 4 thus not divisible by 36.
and, 225078 is not divisible by 4 thus not divisible by 36.
and, 225079 is not divisible by 4 thus not divisible by 36.
Similarly, we can find 225576 & 225972 divisible by 36.
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Use properties of operations to write an equivalent expression to 17n+9−47n.
A: 9−37n
B: 9−57n
c: 9+37n
D: 9+57n
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{17n + 9 - 47n}[/tex]
[tex]\huge\textbf{COMBINE the LIKE TERMS}[/tex]
[tex]\mathsf{= (17n - 47n) + (9)}[/tex]
[tex]\mathsf{= 17n - 47n + 9}[/tex]
[tex]\mathsf{= -30n + 9}[/tex]
[tex]\huge\text{Therefore, your answer SHOULD be:}[/tex]
[tex]\huge\boxed{\mathsf{-30n + 9}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Instructors at a sports club were surveyed about whether they are certified in CPR. The survey results are shown in the two-way frequency table.
Does the data show an association between the type of instructor and a certification in CPR? PLEASE I NEED HELP
Answer: The data shows an association between the type of instructor and a certification in CPR. The association is that swimming instructors are less likely than tennis instructors to be certified in CPR. This can be seen from the frequency table, where all the swimming instructors are not certified in CPR, while only 4 out of 12 tennis instructors are not certified in CPR, so yes, the data does show an association between the type of instructor and a certification in CPR.
Step-by-step explanation:
The two-way frequency table shows the number of instructors who are certified or not certified in CPR, broken down by type of instructor (swimming or tennis). The data in the table allows us to see the relationship between the two variables (type of instructor and certification in CPR) and whether there is an association between them.
An association means that the values of one variable are related to the values of another variable in some way. In this case, the type of instructor (swimming or tennis) is related to whether or not the instructor is certified in CPR. The data shows that the proportion of swimming instructors who are not certified in CPR (100%) is higher than the proportion of tennis instructors who are not certified in CPR (33%). This indicates that there is an association between type of instructor and certification in CPR, with swimming instructors being less likely to be certified in CPR than tennis instructors.
It is important to note that this association does not necessarily imply causation, meaning that being a swimming instructor does not cause one to not be certified in CPR, but it could be the other way around, or it could be due to some other factors that the data does not show.
Ella bought 10 packs of cups for her holiday party. A medium size pack of cups cost $1.80, while a large one costs $2.40. If she spent $21.60, how many packs of each type did she buy?
Answer:
Step-by-step explanation:
2.40X+1.80(10-X)=21.602.40X+18-1.8X=21.60.6X=21.60-18.6X=3.6X=3.6/.6X=6 PACKS OF $2.40 CUPS.
8 _ 6 _ 4 _ 2=6 you can use - ,+, x
Answer:
[tex]+, -, \times[/tex]
Step-by-step explanation:
This is one of those questions where trial and error are used.
Trying out different combos until I get the right answer:
[tex]8-6+4\times2=10[/tex]
[tex]8+6-4\times2=6[/tex]
Nice! The correct answer is [tex]+, -, \times[/tex]
-6+7x≤-22
plss help me
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
Inequality Form:
x≤−16/7
Interval Notation:
(−∞,−16/7]
The solution to the linear inequality given as -6 + 7x ≤ -22 is determined as x ≤ -16/7.
What is the value of x in the inequality?The value of x in the inequality -6 + 7x ≤ -22, is determined by applying the following method.
The given inequality expression;
-6 + 7x ≤ -22
Solve the inequality by collecting similar terms together as shown below;
-6 + 7x + 6 ≤ -22 + 6
Simplify further as follows;
7x ≤ -16
Divide both sides of the inequality by 7 to solve for x as shown below;
(7x)/7 ≤ (-16)/7
x ≤ -16/7
Therefore, the solution to the inequality is x ≤ -16/7.
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Abdoulaye is taking a multiple choice test with a total of 50 points available. Each question is worth exactly 2 points. What would be Abdoulaye's test score (out of 50) if he got 5 questions wrong? What would be his score if he got
x
x questions wrong?
Answer: 40 and 50-2x.
Step-by-step explanation: you multiply 5*2=10, and subtract that from 50. You would do the same with x, to get 2*x=2x. but you can't subtract 2x from 50 without knowing x, so you leave it as 50-2x.
The solution of the equation ax + b = 0 [ a isint equal to is ______
A number is between 15 and 20. It has prime factors of 2 and 3. What is the number?
The number is given by the equation A = 18
What are Factors of a Number?Numbers that divide an original number evenly or precisely are known as its factors. A factor is a whole number that can divide a larger number in two equal parts. A factor is a number that divides another number, leaving no remainder
Given data ,
Let the inequality be represented as A
Now , the value of A is
15 < A < 20 be equation (1)
The number lies between 15 and 20
when A = 18
The factors of 18 = 1 , 2 , 3 , 6 , 9 , 18
So , the number 18 has the prime factors as 2 and 3
Hence , the number is A = 18
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Paid $53. 99 for a 40 lb bag of dog food at Cotco. At Target, they are elling the ame dog food for $28. 99 for a 20 lb bag. Find the unit price in dollar per pound. Then tate which bag of dog food i the better buy baed on the unit price. ]
Since the unit price per pound of the dog food we bought is lesser than that of Target, we got a better buy.
To find the unit price per pound, we need to divide the price paid by the amount bought (in pounds)
`Now we have paid $53.99 for 40 pounds
Target charges $28.99 for 20 pounds.
Hence the unit price per pound we paid will be
53.99/40
= $1.34975 /lb
Now the unit price per pound charged by Target is
$28.99/20 lb
= $ 1.4495 /lb
Hence here we can clearly see 1.34975 < 1.4495
Hence, we bought the dog food at a better price than that at Target.
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Complete Question
I paid $53.99 for a 40 lb bag of dog food at Costco. At Target, they are selling the same dog food for $28.99 for a 20 lb bag. Find the unit price in dollars per pound. Then state which bag of dog food is the better buy based on the unit price.
Please Help!
(This is Recursive Formulas for Algebra II)
The value of the equations are
a₃ = -1
a₄ = -4
a₅ = 5
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of aₙ = - aₙ₋₁ - aₙ₋₂
The value of a₁ = -4
The value of a₂ = 5
So , when n = 3
Substitute the value of n = 3 in the equation , we get
a₃ = -a₂ - a₁
On simplifying the equation , we get
a₃ = -5 - ( -4 )
a₃ = -5 + 4
a₃ = -1
Substitute the value of n = 4 in the equation , we get
a₄ = -a₃ - a₂
On simplifying the equation , we get
a₄ = - ( -1 ) - ( 5 )
a₄ = + 1 - 5
a₄ = -4
Substitute the value of n = 5 in the equation , we get
a₅ = -a₄ - a₃
On simplifying the equation , we get
a₅ = - ( -4 ) - ( -1 )
a₅ = 4 + 1
a₅ = 5
Hence , the equations are solved
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Lex, Mattie, Penelope, and Wallace shares 1/5 pound of candy equally . how much does each person get .which number should go first? THIS IS WHAT YOU WILL CUT UP AND DIVIDE OUT START with 1 /5 CANDY to cut up! START with 4 PEOPLE to cut up!
Help me please .
The amount of candy each person gets is given by the equation A = 1/20 of the candy
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount of candy each person receives is A
Now , the amount of candy = 1/5 of the candy
The number of friends = 4 friends
So , the amount of candy each person gets A = amount of candy / number of friends
Substituting the values in the equation , we get
The amount of candy each person gets A = ( 1/5 ) / 4
On simplifying the equation , we get
The amount of candy each person gets A = 1/20 of the candy
Hence , the equation is A = 1/20
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Maria, a teacher at Learn4Life created a histogram for the vacations she's taken in the last ten years. She hasn't added the 7-day vacation yet she took this summer. Using your pencil, draw and add the 7-day vacation Maria took this summer to the histogram on the right. help help help help help ): please
According to the information, Maria has to add a unit in the second bar that corresponds to the vacations that have between 7 and 9 days.
How to fill in the graph correctly?To complete the graph correctly we must identify what information is in it. First of all we see that there are ranges of duration of vacations on the X axis, then, there are 4 bars that represent the following ranges:
4 - 67 - 910 - 1213 - 15According to the above, since she has not added her last vacation that lasted 7 days, we must add a unit that represents these vacations in the second column, to complete the graph.
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a bag contains 19 balls numbered 1 through 19. what is the probability that a randomly selected ball has a number less than 10?
The probability that a randomly selected ball has a number less than 10 is [tex]$\frac{9}{19}[/tex].
As per the given data:
A bag contains 19 balls numbered 1 through 19.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19
The total number of outcomes is 19.
Here we have to determine the probability that a randomly selected ball has a number less than 10.
Numbers on the balls less than 10 are 1, 2, 3, 4, 5, 6, 7, 8, and 9.
A ball is randomly selected.
The favorable outcomes are 9.
The likelihood of every event depends on the overall number of positive outcomes as well as the number of favorable outcomes.
The formula for probability:
The number of favorable outcomes is divided by the total number of outcomes.
= [tex]$\frac{9}{19}[/tex]
Therefore the probability that a randomly selected ball has a number less than 10 is [tex]$\frac{9}{19}[/tex].
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3. James bought a watch for 48 U.S. dollars. What is the cost of the watch in Swiss francs? Use the conversion formula below. Show your work. Answer: 1 U.S. dollar = 1.02 Swiss francs
3.(part 2) James would like to buy a battery for 10 U.S. dollars. He has 10.20 Swiss francs remaining after buying the watch. On the lines below, determine whether Scott has enough money to buy the battery. Explain how you determined your answer.
Answer:
see below
Step-by-step explanation:
1 U.S. dollar = 1.02 Swiss francs
$48 = CHF 48.96
part 2
CHF 10.20 = US$10
yes he has enough
it is thursday and an angler is planning a fishing trip in two days on saturday. the angler knows from experience that the fishing is best at a particular location at the beginning of high tide. he does not have a tide table, but the angler noted that the high tide on thursday was at 12:15 pm. at what time on saturday should he plan to arrive to start fishing, assuming that this location has a diurnal tide type?
Assuming the location has a diurnal tide type, the angler should plan to arrive to start fishing at 12:15 pm on Saturday, two days after the high tide on Thursday.
This is because with a diurnal tide type, the high tide occurs at the same time each day, so the angler can expect the high tide to occur at the same time on Saturday as it did on Thursday.
A diurnal tide type is a type of tidal pattern where there is one high tide and one low tide per day. This type of tide is most commonly seen in areas with small and shallow bodies of water, such as bays and estuaries. In diurnal tidal systems, the times of high and low tide usually occur at the same time each day. The height of the tide also usually remains relatively constant over time.
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Five litres of paint cost R575 work out the cost of fifteen litres of paint
Answer:
It will cost R1725
The ratio for this problem is 5: 575.
(litres of paint: price)
We first need to figure out how to go from 5 to 15.
5 × 3 = 15To go from 5 to 15, we multiply the 5 by 3.
Now that we have this, we need to multiply the other side of the ratio (575) by 3.
575 × 3 = 1725The ratio now looks like this:
15: 1725
Therefore, for every fifteen litres of paint, it will cost R1725.
an old fashioned record player spins an album at a rate of 33 1/2 rmp ( revolutions per minute) convert this rate into degrees per second
step by step please
Work Shown:
[tex]\frac{33.5 \text{ rev}}{1 \text{ min}} *\frac{360 \text{ deg}}{1 \text{ rev}}*\frac{1 \text{ min}}{60 \text{ sec}} \\\\[/tex]
[tex]=\frac{33.5 \not{\text{r}}\not{\text{e}}\not{\text{v}}}{1 \text{ min}} *\frac{360 \text{ deg}}{1 \not{\text{r}}\not{\text{e}}\not{\text{v}}}*\frac{1 \text{ min}}{60 \text{ sec}} \ \text{ ... 'rev' units cancel}\\\\[/tex]
[tex]=\frac{33.5}{1 \text{ min}} *\frac{360 \text{ deg}}{1}*\frac{1 \text{ min}}{60 \text{ sec}} \\\\[/tex]
[tex]=\frac{33.5}{1 \not{\text{m}}\not{\text{i}}\not{\text{n}}} *\frac{360 \text{ deg}}{1}*\frac{1 \not{\text{m}}\not{\text{i}}\not{\text{n}}}{60 \text{ sec}} \ \ \text{ ... 'min' units cancel}\\\\[/tex]
[tex]=\frac{33.5}{1} *\frac{360 \text{ deg}}{1}*\frac{1}{60 \text{ sec}}\\\\[/tex]
[tex]=\frac{33.5*360}{60} \text{ degrees per second}[/tex]
[tex]=201 \text{ degrees per second}[/tex]
Notes:
1 revolution = a full 360 degree turnrpm = revolutions per minuteThe ladder on a fire truck is 70ft long. If the ladder is 25ft from the base of a building, how far up the building can the ladder reach? Round your answer to the nearest hundredth.
Using the Pythagorean Theorem we know that the ladder can reach up to the building 85ft.
What is Pythagorean Theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental Euclidean geometry relationship between the three sides of a right triangle.
This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
So, we have:
Hypotuenese is 70ft long and Height is 25ft long.
Then, the base would be:
c² = a² + b²
70² = 25² + b²
b² = 4,900 - 625
b² = 7,275
b = √7275
b = 85ft
Therefore, using the Pythagorean Theorem we know that the ladder can reach up to the building 85ft.
Know more about the Pythagorean Theorem here:
https://brainly.com/question/343682
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